Generating a Double-Scroll Attractor by Connecting a Pair of Mutual Mirror-Image Attractors via Planar Switching Control

Abstract

An original three-dimensional (3D) smooth continuous chaotic system and its mirror-image system with eight common parameters are constructed and a pair of symmetric chaotic attractors can be generated simultaneously. Basic dynamical behaviors of two 3D chaotic systems are investigated respectively. A double-scroll chaotic attractor by connecting the pair of mutual mirror-image attractors is generated via a novel planar switching control approach. Chaos can also be controlled to a fixed point, a periodic orbit and a divergent orbit respectively by switching between two chaotic systems. Finally, an equivalent 3D chaotic system by combining two 3D chaotic systems with a switching law is designed by utilizing a sign function. Two circuit diagrams for realizing the double-scroll attractor are depicted by employing an improved module-based design approach.